Advertisement

Ukrainian Mathematical Journal

, Volume 70, Issue 7, pp 1075–1096 | Cite as

ORV Sequences with Nondegenerate Groups of Regular Points

  • V. V. Pavlenkov
Article
  • 1 Downloads

We define a class of ORV sequences with nondegenerate groups of regular points and consider some properties of these sequences.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    S. Aljancić and D. Arandelović, “O-regularly varying functions,” Publ. Inst. Math. (Beograd), 22, 5–22 (1977).MathSciNetzbMATHGoogle Scholar
  2. 2.
    V. G. Avakumovic, “Sur une extension de la condition de convergence des théorèmes inverses de sommabilité,” C. R. Acad. Sci. Paris, 200, 1515–1517 (1935).zbMATHGoogle Scholar
  3. 3.
    N. M. Bingham, C. M. Goldie, and J. L. Teugels, Regular Variation, Cambridge Univ. Press, Cambridge (1987).CrossRefGoogle Scholar
  4. 4.
    R. Bojanic and E. Seneta, “A unified theory of regularly varying sequences,” Math. Z., 134, 91–106 (1973).MathSciNetCrossRefGoogle Scholar
  5. 5.
    V. V. Buldyhin, K.-H. Indlekofer, O. I. Klesov, and J. G. Steinebach, Pseudoregular Functions and Generalized Renewal Processes [in Ukrainian], TVIMS, Kyiv (2012).Google Scholar
  6. 6.
    V. V. Buldyhin, O. I. Klesov, and J. G. Steinebach, “Some properties of asymptotically quasiinvertible functions and their application. I,” Teor. Imovir. Mat. Statyst., 70, 9–25 (2004).Google Scholar
  7. 7.
    V. V. Buldygin, O. I. Klesov, and J. G. Steinebach, “On factorization representation for Avakumovic–Karamata functions with nondegenerate groups of regular points,” Anal. Math., 30, 161–192 (2004).MathSciNetCrossRefGoogle Scholar
  8. 8.
    D. Drasin and E. Seneta, “A generalization of slowly varying functions,” Proc. Amer. Math. Soc., 96, 470–472 (1986).MathSciNetCrossRefGoogle Scholar
  9. 9.
    J. Galambos and E. Seneta, “Regularly varying sequences,” Proc. Amer. Math. Soc., 41, 110–116 (1973).MathSciNetCrossRefGoogle Scholar
  10. 10.
    J. Karamata, “Sur certains ‘Tauberian theorems’ de M. M. Hardy et Littlewood,” Mathematica (Cluj), 3, 33–48 (1930).Google Scholar
  11. 11.
    J. Karamata, “Sur un mode de croissance régulière,” Mathematica (Cluj), 4, 38–53 (1930).zbMATHGoogle Scholar
  12. 12.
    J. Karamata, “Sur un mode de croissance régulière. Théorèmes fondamentaux,” Bull. Soc. Math. France, 61, 55–62 (1933).MathSciNetCrossRefGoogle Scholar
  13. 13.
    J. Kubilius, Probabilistic Method in the Theory of Numbers, American Mathematical Society, Providence, RI (1964).Google Scholar
  14. 14.
    I. Weissman, “A note on Bojanic–Seneta theory of regularly varying sequences,” Math. Z., 151, 29–30 (1976).MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • V. V. Pavlenkov
    • 1
  1. 1.“Sikorski Kyiv Polytechnic Institute” Ukrainian National Technical UniversityKyivUkraine

Personalised recommendations